% Mizar ND problem: t2_anproj_2,anproj_2,87,43 
fof(dh_c1_3__anproj_2,definition,
    ( ( ( ~ v3_struct_0(c1_3__anproj_2)
        & v3_rlvect_1(c1_3__anproj_2)
        & v4_rlvect_1(c1_3__anproj_2)
        & v5_rlvect_1(c1_3__anproj_2)
        & v6_rlvect_1(c1_3__anproj_2)
        & v7_rlvect_1(c1_3__anproj_2)
        & l2_rlvect_1(c1_3__anproj_2) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_3__anproj_2))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_3__anproj_2))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(c1_3__anproj_2))
                     => ( ! [E] : 
                            ( m1_subset_1(E,k1_numbers)
                           => ! [F] : 
                                ( m1_subset_1(F,k1_numbers)
                               => ! [G] : 
                                    ( m1_subset_1(G,k1_numbers)
                                   => ! [H] : 
                                        ( m1_subset_1(H,k1_numbers)
                                       => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,A,E),k3_rlvect_1(c1_3__anproj_2,B,F)),k3_rlvect_1(c1_3__anproj_2,C,G)),k3_rlvect_1(c1_3__anproj_2,D,H)) = k1_rlvect_1(c1_3__anproj_2)
                                         => ( E = 0
                                            & F = 0
                                            & G = 0
                                            & H = 0 ) ) ) ) ) )
                       => ( v8_rlvect_1(A,c1_3__anproj_2)
                          & v8_rlvect_1(B,c1_3__anproj_2)
                          & ~ r1_anproj_1(c1_3__anproj_2,A,B)
                          & v8_rlvect_1(C,c1_3__anproj_2)
                          & v8_rlvect_1(D,c1_3__anproj_2)
                          & ~ r1_anproj_1(c1_3__anproj_2,C,D)
                          & ~ r2_anproj_1(c1_3__anproj_2,A,B,C)
                          & ~ r2_anproj_1(c1_3__anproj_2,C,D,A) ) ) ) ) ) ) )
   => ! [I] : 
        ( ( ~ v3_struct_0(I)
          & v3_rlvect_1(I)
          & v4_rlvect_1(I)
          & v5_rlvect_1(I)
          & v6_rlvect_1(I)
          & v7_rlvect_1(I)
          & l2_rlvect_1(I) )
       => ! [J] : 
            ( m1_subset_1(J,u1_struct_0(I))
           => ! [K] : 
                ( m1_subset_1(K,u1_struct_0(I))
               => ! [L] : 
                    ( m1_subset_1(L,u1_struct_0(I))
                   => ! [M] : 
                        ( m1_subset_1(M,u1_struct_0(I))
                       => ( ! [N] : 
                              ( m1_subset_1(N,k1_numbers)
                             => ! [O] : 
                                  ( m1_subset_1(O,k1_numbers)
                                 => ! [P] : 
                                      ( m1_subset_1(P,k1_numbers)
                                     => ! [Q] : 
                                          ( m1_subset_1(Q,k1_numbers)
                                         => ( k4_rlvect_1(I,k4_rlvect_1(I,k4_rlvect_1(I,k3_rlvect_1(I,J,N),k3_rlvect_1(I,K,O)),k3_rlvect_1(I,L,P)),k3_rlvect_1(I,M,Q)) = k1_rlvect_1(I)
                                           => ( N = 0
                                              & O = 0
                                              & P = 0
                                              & Q = 0 ) ) ) ) ) )
                         => ( v8_rlvect_1(J,I)
                            & v8_rlvect_1(K,I)
                            & ~ r1_anproj_1(I,J,K)
                            & v8_rlvect_1(L,I)
                            & v8_rlvect_1(M,I)
                            & ~ r1_anproj_1(I,L,M)
                            & ~ r2_anproj_1(I,J,K,L)
                            & ~ r2_anproj_1(I,L,M,J) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__anproj_2),file(anproj_2,c1_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c1_3__anproj_2)]).

fof(dh_c2_3__anproj_2,definition,
    ( ( m1_subset_1(c2_3__anproj_2,u1_struct_0(c1_3__anproj_2))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_3__anproj_2))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_3__anproj_2))
                 => ( ! [D] : 
                        ( m1_subset_1(D,k1_numbers)
                       => ! [E] : 
                            ( m1_subset_1(E,k1_numbers)
                           => ! [F] : 
                                ( m1_subset_1(F,k1_numbers)
                               => ! [G] : 
                                    ( m1_subset_1(G,k1_numbers)
                                   => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,D),k3_rlvect_1(c1_3__anproj_2,A,E)),k3_rlvect_1(c1_3__anproj_2,B,F)),k3_rlvect_1(c1_3__anproj_2,C,G)) = k1_rlvect_1(c1_3__anproj_2)
                                     => ( D = 0
                                        & E = 0
                                        & F = 0
                                        & G = 0 ) ) ) ) ) )
                   => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
                      & v8_rlvect_1(A,c1_3__anproj_2)
                      & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,A)
                      & v8_rlvect_1(B,c1_3__anproj_2)
                      & v8_rlvect_1(C,c1_3__anproj_2)
                      & ~ r1_anproj_1(c1_3__anproj_2,B,C)
                      & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,A,B)
                      & ~ r2_anproj_1(c1_3__anproj_2,B,C,c2_3__anproj_2) ) ) ) ) ) )
   => ! [H] : 
        ( m1_subset_1(H,u1_struct_0(c1_3__anproj_2))
       => ! [I] : 
            ( m1_subset_1(I,u1_struct_0(c1_3__anproj_2))
           => ! [J] : 
                ( m1_subset_1(J,u1_struct_0(c1_3__anproj_2))
               => ! [K] : 
                    ( m1_subset_1(K,u1_struct_0(c1_3__anproj_2))
                   => ( ! [L] : 
                          ( m1_subset_1(L,k1_numbers)
                         => ! [M] : 
                              ( m1_subset_1(M,k1_numbers)
                             => ! [N] : 
                                  ( m1_subset_1(N,k1_numbers)
                                 => ! [O] : 
                                      ( m1_subset_1(O,k1_numbers)
                                     => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,H,L),k3_rlvect_1(c1_3__anproj_2,I,M)),k3_rlvect_1(c1_3__anproj_2,J,N)),k3_rlvect_1(c1_3__anproj_2,K,O)) = k1_rlvect_1(c1_3__anproj_2)
                                       => ( L = 0
                                          & M = 0
                                          & N = 0
                                          & O = 0 ) ) ) ) ) )
                     => ( v8_rlvect_1(H,c1_3__anproj_2)
                        & v8_rlvect_1(I,c1_3__anproj_2)
                        & ~ r1_anproj_1(c1_3__anproj_2,H,I)
                        & v8_rlvect_1(J,c1_3__anproj_2)
                        & v8_rlvect_1(K,c1_3__anproj_2)
                        & ~ r1_anproj_1(c1_3__anproj_2,J,K)
                        & ~ r2_anproj_1(c1_3__anproj_2,H,I,J)
                        & ~ r2_anproj_1(c1_3__anproj_2,J,K,H) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_3__anproj_2),file(anproj_2,c2_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c2_3__anproj_2)]).

fof(dh_c3_3__anproj_2,definition,
    ( ( m1_subset_1(c3_3__anproj_2,u1_struct_0(c1_3__anproj_2))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_3__anproj_2))
             => ( ! [C] : 
                    ( m1_subset_1(C,k1_numbers)
                   => ! [D] : 
                        ( m1_subset_1(D,k1_numbers)
                       => ! [E] : 
                            ( m1_subset_1(E,k1_numbers)
                           => ! [F] : 
                                ( m1_subset_1(F,k1_numbers)
                               => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,C),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,D)),k3_rlvect_1(c1_3__anproj_2,A,E)),k3_rlvect_1(c1_3__anproj_2,B,F)) = k1_rlvect_1(c1_3__anproj_2)
                                 => ( C = 0
                                    & D = 0
                                    & E = 0
                                    & F = 0 ) ) ) ) ) )
               => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
                  & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
                  & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
                  & v8_rlvect_1(A,c1_3__anproj_2)
                  & v8_rlvect_1(B,c1_3__anproj_2)
                  & ~ r1_anproj_1(c1_3__anproj_2,A,B)
                  & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,A)
                  & ~ r2_anproj_1(c1_3__anproj_2,A,B,c2_3__anproj_2) ) ) ) ) )
   => ! [G] : 
        ( m1_subset_1(G,u1_struct_0(c1_3__anproj_2))
       => ! [H] : 
            ( m1_subset_1(H,u1_struct_0(c1_3__anproj_2))
           => ! [I] : 
                ( m1_subset_1(I,u1_struct_0(c1_3__anproj_2))
               => ( ! [J] : 
                      ( m1_subset_1(J,k1_numbers)
                     => ! [K] : 
                          ( m1_subset_1(K,k1_numbers)
                         => ! [L] : 
                              ( m1_subset_1(L,k1_numbers)
                             => ! [M] : 
                                  ( m1_subset_1(M,k1_numbers)
                                 => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,J),k3_rlvect_1(c1_3__anproj_2,G,K)),k3_rlvect_1(c1_3__anproj_2,H,L)),k3_rlvect_1(c1_3__anproj_2,I,M)) = k1_rlvect_1(c1_3__anproj_2)
                                   => ( J = 0
                                      & K = 0
                                      & L = 0
                                      & M = 0 ) ) ) ) ) )
                 => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
                    & v8_rlvect_1(G,c1_3__anproj_2)
                    & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,G)
                    & v8_rlvect_1(H,c1_3__anproj_2)
                    & v8_rlvect_1(I,c1_3__anproj_2)
                    & ~ r1_anproj_1(c1_3__anproj_2,H,I)
                    & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,G,H)
                    & ~ r2_anproj_1(c1_3__anproj_2,H,I,c2_3__anproj_2) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_3__anproj_2),file(anproj_2,c3_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c3_3__anproj_2)]).

fof(dh_c4_3__anproj_2,definition,
    ( ( m1_subset_1(c4_3__anproj_2,u1_struct_0(c1_3__anproj_2))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
         => ( ! [B] : 
                ( m1_subset_1(B,k1_numbers)
               => ! [C] : 
                    ( m1_subset_1(C,k1_numbers)
                   => ! [D] : 
                        ( m1_subset_1(D,k1_numbers)
                       => ! [E] : 
                            ( m1_subset_1(E,k1_numbers)
                           => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,B),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,C)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,D)),k3_rlvect_1(c1_3__anproj_2,A,E)) = k1_rlvect_1(c1_3__anproj_2)
                             => ( B = 0
                                & C = 0
                                & D = 0
                                & E = 0 ) ) ) ) ) )
           => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
              & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
              & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
              & v8_rlvect_1(c4_3__anproj_2,c1_3__anproj_2)
              & v8_rlvect_1(A,c1_3__anproj_2)
              & ~ r1_anproj_1(c1_3__anproj_2,c4_3__anproj_2,A)
              & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,c4_3__anproj_2)
              & ~ r2_anproj_1(c1_3__anproj_2,c4_3__anproj_2,A,c2_3__anproj_2) ) ) ) )
   => ! [F] : 
        ( m1_subset_1(F,u1_struct_0(c1_3__anproj_2))
       => ! [G] : 
            ( m1_subset_1(G,u1_struct_0(c1_3__anproj_2))
           => ( ! [H] : 
                  ( m1_subset_1(H,k1_numbers)
                 => ! [I] : 
                      ( m1_subset_1(I,k1_numbers)
                     => ! [J] : 
                          ( m1_subset_1(J,k1_numbers)
                         => ! [K] : 
                              ( m1_subset_1(K,k1_numbers)
                             => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,H),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,I)),k3_rlvect_1(c1_3__anproj_2,F,J)),k3_rlvect_1(c1_3__anproj_2,G,K)) = k1_rlvect_1(c1_3__anproj_2)
                               => ( H = 0
                                  & I = 0
                                  & J = 0
                                  & K = 0 ) ) ) ) ) )
             => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
                & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
                & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
                & v8_rlvect_1(F,c1_3__anproj_2)
                & v8_rlvect_1(G,c1_3__anproj_2)
                & ~ r1_anproj_1(c1_3__anproj_2,F,G)
                & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,F)
                & ~ r2_anproj_1(c1_3__anproj_2,F,G,c2_3__anproj_2) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_3__anproj_2),file(anproj_2,c4_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c4_3__anproj_2)]).

fof(dh_c5_3__anproj_2,definition,
    ( ( m1_subset_1(c5_3__anproj_2,u1_struct_0(c1_3__anproj_2))
     => ( ! [A] : 
            ( m1_subset_1(A,k1_numbers)
           => ! [B] : 
                ( m1_subset_1(B,k1_numbers)
               => ! [C] : 
                    ( m1_subset_1(C,k1_numbers)
                   => ! [D] : 
                        ( m1_subset_1(D,k1_numbers)
                       => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,A),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,B)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,C)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,D)) = k1_rlvect_1(c1_3__anproj_2)
                         => ( A = 0
                            & B = 0
                            & C = 0
                            & D = 0 ) ) ) ) ) )
       => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
          & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
          & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
          & v8_rlvect_1(c4_3__anproj_2,c1_3__anproj_2)
          & v8_rlvect_1(c5_3__anproj_2,c1_3__anproj_2)
          & ~ r1_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2)
          & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,c4_3__anproj_2)
          & ~ r2_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2,c2_3__anproj_2) ) ) )
   => ! [E] : 
        ( m1_subset_1(E,u1_struct_0(c1_3__anproj_2))
       => ( ! [F] : 
              ( m1_subset_1(F,k1_numbers)
             => ! [G] : 
                  ( m1_subset_1(G,k1_numbers)
                 => ! [H] : 
                      ( m1_subset_1(H,k1_numbers)
                     => ! [I] : 
                          ( m1_subset_1(I,k1_numbers)
                         => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,F),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,G)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,H)),k3_rlvect_1(c1_3__anproj_2,E,I)) = k1_rlvect_1(c1_3__anproj_2)
                           => ( F = 0
                              & G = 0
                              & H = 0
                              & I = 0 ) ) ) ) ) )
         => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
            & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
            & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
            & v8_rlvect_1(c4_3__anproj_2,c1_3__anproj_2)
            & v8_rlvect_1(E,c1_3__anproj_2)
            & ~ r1_anproj_1(c1_3__anproj_2,c4_3__anproj_2,E)
            & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,c4_3__anproj_2)
            & ~ r2_anproj_1(c1_3__anproj_2,c4_3__anproj_2,E,c2_3__anproj_2) ) ) ) ),
    introduced(definition,[new_symbol(c5_3__anproj_2),file(anproj_2,c5_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c5_3__anproj_2)]).

fof(e1_3__anproj_2,assumption,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_subset_1(D,k1_numbers)
                 => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,A),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,B)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,C)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,D)) = k1_rlvect_1(c1_3__anproj_2)
                   => ( A = 0
                      & B = 0
                      & C = 0
                      & D = 0 ) ) ) ) ) ) ),
    introduced(assumption,[file(anproj_2,e1_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,e1_3__anproj_2)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(rc5_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_1)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    [interesting(0.9),axiom,file(struct_0,l2_struct_0)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k2_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k2_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k2_rlvect_1)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_1)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    [interesting(0.9),axiom,file(struct_0,l2_struct_0)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(rc4_struct_0,theorem,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc4_struct_0)]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(commutativity_k4_rlvect_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ),
    file(rlvect_1,k4_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]).

fof(symmetry_r1_anproj_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r1_anproj_1(A,B,C)
       => r1_anproj_1(A,C,B) ) ) ),
    file(anproj_1,r1_anproj_1),
    [interesting(0.9),axiom,file(anproj_1,r1_anproj_1)]).

fof(reflexivity_r1_anproj_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r1_anproj_1(A,B,B) ) ),
    file(anproj_1,r1_anproj_1),
    [interesting(0.9),axiom,file(anproj_1,r1_anproj_1)]).

fof(existence_l2_rlvect_1,axiom,(
    ? [A] : l2_rlvect_1(A) ),
    file(rlvect_1,l2_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_1)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(redefinition_k4_rlvect_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ),
    file(rlvect_1,k4_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k1_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ),
    file(rlvect_1,k1_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k1_rlvect_1)]).

fof(dt_k3_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_numbers) )
     => m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k3_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k3_rlvect_1)]).

fof(dt_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k4_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]).

fof(dt_l2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_rlvect_1(A)
     => l1_rlvect_1(A) ) ),
    file(rlvect_1,l2_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_3__anproj_2,assumption,
    ( ~ v3_struct_0(c1_3__anproj_2)
    & v3_rlvect_1(c1_3__anproj_2)
    & v4_rlvect_1(c1_3__anproj_2)
    & v5_rlvect_1(c1_3__anproj_2)
    & v6_rlvect_1(c1_3__anproj_2)
    & v7_rlvect_1(c1_3__anproj_2)
    & l2_rlvect_1(c1_3__anproj_2) ),
    introduced(assumption,[file(anproj_2,c1_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c1_3__anproj_2)]).

fof(dt_c2_3__anproj_2,assumption,(
    m1_subset_1(c2_3__anproj_2,u1_struct_0(c1_3__anproj_2)) ),
    introduced(assumption,[file(anproj_2,c2_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c2_3__anproj_2)]).

fof(dt_c3_3__anproj_2,assumption,(
    m1_subset_1(c3_3__anproj_2,u1_struct_0(c1_3__anproj_2)) ),
    introduced(assumption,[file(anproj_2,c3_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c3_3__anproj_2)]).

fof(dt_c4_3__anproj_2,assumption,(
    m1_subset_1(c4_3__anproj_2,u1_struct_0(c1_3__anproj_2)) ),
    introduced(assumption,[file(anproj_2,c4_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c4_3__anproj_2)]).

fof(dt_c5_3__anproj_2,assumption,(
    m1_subset_1(c5_3__anproj_2,u1_struct_0(c1_3__anproj_2)) ),
    introduced(assumption,[file(anproj_2,c5_3__anproj_2)]),
    [interesting(0.8),axiom,file(anproj_2,c5_3__anproj_2)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

fof(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(dh_c1_3_2__anproj_2,definition,
    ( ( m1_subset_1(c1_3_2__anproj_2,k1_numbers)
     => ! [A] : 
          ( m1_subset_1(A,k1_numbers)
         => ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,A)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,B)) = k1_rlvect_1(c1_3__anproj_2)
               => ( c1_3_2__anproj_2 = 0
                  & A = 0
                  & B = 0 ) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,k1_numbers)
       => ! [D] : 
            ( m1_subset_1(D,k1_numbers)
           => ! [E] : 
                ( m1_subset_1(E,k1_numbers)
               => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,C),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,D)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,E)) = k1_rlvect_1(c1_3__anproj_2)
                 => ( C = 0
                    & D = 0
                    & E = 0 ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3_2__anproj_2),file(anproj_2,c1_3_2__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c1_3_2__anproj_2)]).

fof(dh_c2_3_2__anproj_2,definition,
    ( ( m1_subset_1(c2_3_2__anproj_2,k1_numbers)
     => ! [A] : 
          ( m1_subset_1(A,k1_numbers)
         => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,A)) = k1_rlvect_1(c1_3__anproj_2)
           => ( c1_3_2__anproj_2 = 0
              & c2_3_2__anproj_2 = 0
              & A = 0 ) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k1_numbers)
       => ! [C] : 
            ( m1_subset_1(C,k1_numbers)
           => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,B)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,C)) = k1_rlvect_1(c1_3__anproj_2)
             => ( c1_3_2__anproj_2 = 0
                & B = 0
                & C = 0 ) ) ) ) ),
    introduced(definition,[new_symbol(c2_3_2__anproj_2),file(anproj_2,c2_3_2__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c2_3_2__anproj_2)]).

fof(dh_c3_3_2__anproj_2,definition,
    ( ( m1_subset_1(c3_3_2__anproj_2,k1_numbers)
     => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c3_3_2__anproj_2)) = k1_rlvect_1(c1_3__anproj_2)
       => ( c1_3_2__anproj_2 = 0
          & c2_3_2__anproj_2 = 0
          & c3_3_2__anproj_2 = 0 ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_numbers)
       => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,A)) = k1_rlvect_1(c1_3__anproj_2)
         => ( c1_3_2__anproj_2 = 0
            & c2_3_2__anproj_2 = 0
            & A = 0 ) ) ) ),
    introduced(definition,[new_symbol(c3_3_2__anproj_2),file(anproj_2,c3_3_2__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c3_3_2__anproj_2)]).

fof(e1_3_2__anproj_2,assumption,(
    k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c3_3_2__anproj_2)) = k1_rlvect_1(c1_3__anproj_2) ),
    introduced(assumption,[file(anproj_2,e1_3_2__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,e1_3_2__anproj_2)]).

fof(dt_c1_3_2__anproj_2,assumption,(
    m1_subset_1(c1_3_2__anproj_2,k1_numbers) ),
    introduced(assumption,[file(anproj_2,c1_3_2__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c1_3_2__anproj_2)]).

fof(dt_c2_3_2__anproj_2,assumption,(
    m1_subset_1(c2_3_2__anproj_2,k1_numbers) ),
    introduced(assumption,[file(anproj_2,c2_3_2__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c2_3_2__anproj_2)]).

fof(dt_c3_3_2__anproj_2,assumption,(
    m1_subset_1(c3_3_2__anproj_2,k1_numbers) ),
    introduced(assumption,[file(anproj_2,c3_3_2__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c3_3_2__anproj_2)]).

fof(t10_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
            & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ),
    file(rlvect_1,t10_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,t10_rlvect_1)]).

fof(e1_3_2_1__anproj_2,plain,(
    k1_rlvect_1(c1_3__anproj_2) = k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c3_3_2__anproj_2)),k1_rlvect_1(c1_3__anproj_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c3_3_2__anproj_2,dt_c4_3__anproj_2,e1_3_2__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,fc6_membered,rc1_membered,t1_subset,cc10_membered,cc11_membered,cc15_membered,cc4_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,dt_k1_numbers,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k2_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c3_3_2__anproj_2,dt_c4_3__anproj_2,e1_3_2__anproj_2,t10_rlvect_1]),
    [interesting(0.5),file(anproj_2,e1_3_2_1__anproj_2),[file(anproj_2,e1_3_2_1__anproj_2)]]).

fof(t23_rlvect_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ( ( A = 0
                  | C = k1_rlvect_1(B) )
               => k3_rlvect_1(B,C,A) = k1_rlvect_1(B) ) ) ) ) ),
    file(rlvect_1,t23_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,t23_rlvect_1)]).

fof(e2_3_2_1__anproj_2,plain,(
    k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c3_3_2__anproj_2)),k1_rlvect_1(c1_3__anproj_2)) = k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c3_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c3_3_2__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c3_3_2__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,fc2_membered,spc0_numerals,spc0_boole,t23_rlvect_1]),
    [interesting(0.5),file(anproj_2,e2_3_2_1__anproj_2),[file(anproj_2,e2_3_2_1__anproj_2)]]).

fof(e2_3_2__anproj_2,plain,(
    k1_rlvect_1(c1_3__anproj_2) = k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c3_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,0)) ),
    inference(iterative_eq,[status(thm),assumptions([e1_3_2__anproj_2,dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c3_3_2__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2])],[e1_3_2_1__anproj_2,e2_3_2_1__anproj_2]),
    [interesting(0.65),file(anproj_2,e2_3_2__anproj_2),[file(anproj_2,e2_3_2__anproj_2)]]).

fof(e3_3_2__anproj_2,plain,
    ( c1_3_2__anproj_2 = 0
    & c2_3_2__anproj_2 = 0
    & c3_3_2__anproj_2 = 0 ),
    inference(mizar_by,[status(thm),assumptions([e1_3_2__anproj_2,dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c3_3_2__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l2_rlvect_1,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c3_3_2__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,fc2_membered,spc0_numerals,spc0_boole,e2_3_2__anproj_2,e1_3__anproj_2]),
    [interesting(0.65),file(anproj_2,e3_3_2__anproj_2),[file(anproj_2,e3_3_2__anproj_2)]]).

fof(i5_3_2__anproj_2,theorem,(
    $true ),
    introduced(tautology,[file(anproj_2,i5_3_2__anproj_2)]),
    [interesting(0.65),trivial,file(anproj_2,i5_3_2__anproj_2)]).

fof(i4_3_2__anproj_2,plain,
    ( c1_3_2__anproj_2 = 0
    & c2_3_2__anproj_2 = 0
    & c3_3_2__anproj_2 = 0 ),
    inference(conclusion,[status(thm),assumptions([e1_3_2__anproj_2,dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c3_3_2__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[e3_3_2__anproj_2,i5_3_2__anproj_2]),
    [interesting(0.65),file(anproj_2,i4_3_2__anproj_2),[file(anproj_2,i4_3_2__anproj_2)]]).

fof(i3_3_2__anproj_2,plain,
    ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c3_3_2__anproj_2)) = k1_rlvect_1(c1_3__anproj_2)
   => ( c1_3_2__anproj_2 = 0
      & c2_3_2__anproj_2 = 0
      & c3_3_2__anproj_2 = 0 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c3_3_2__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2]),discharge_asm(discharge,[e1_3_2__anproj_2])],[e1_3_2__anproj_2,i4_3_2__anproj_2]),
    [interesting(0.65),file(anproj_2,i3_3_2__anproj_2),[file(anproj_2,i3_3_2__anproj_2)]]).

fof(i3_3_2_tmp__anproj_2,plain,
    ( m1_subset_1(c3_3_2__anproj_2,k1_numbers)
   => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c3_3_2__anproj_2)) = k1_rlvect_1(c1_3__anproj_2)
     => ( c1_3_2__anproj_2 = 0
        & c2_3_2__anproj_2 = 0
        & c3_3_2__anproj_2 = 0 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2]),discharge_asm(discharge,[dt_c3_3_2__anproj_2])],[dt_c3_3_2__anproj_2,i3_3_2__anproj_2]),
    [interesting(0.65),i2_3_2__anproj_2]).

fof(i2_3_2__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,A)) = k1_rlvect_1(c1_3__anproj_2)
       => ( c1_3_2__anproj_2 = 0
          & c2_3_2__anproj_2 = 0
          & A = 0 ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c2_3_2__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[i3_3_2_tmp__anproj_2,dh_c3_3_2__anproj_2]),
    [interesting(0.65),file(anproj_2,i2_3_2__anproj_2),[file(anproj_2,i2_3_2__anproj_2)]]).

fof(i2_3_2_tmp__anproj_2,plain,
    ( m1_subset_1(c2_3_2__anproj_2,k1_numbers)
   => ! [A] : 
        ( m1_subset_1(A,k1_numbers)
       => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,c2_3_2__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,A)) = k1_rlvect_1(c1_3__anproj_2)
         => ( c1_3_2__anproj_2 = 0
            & c2_3_2__anproj_2 = 0
            & A = 0 ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2]),discharge_asm(discharge,[dt_c2_3_2__anproj_2])],[dt_c2_3_2__anproj_2,i2_3_2__anproj_2]),
    [interesting(0.65),i1_3_2__anproj_2]).

fof(i1_3_2__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,A)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,B)) = k1_rlvect_1(c1_3__anproj_2)
           => ( c1_3_2__anproj_2 = 0
              & A = 0
              & B = 0 ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_2__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[i2_3_2_tmp__anproj_2,dh_c2_3_2__anproj_2]),
    [interesting(0.65),file(anproj_2,i1_3_2__anproj_2),[file(anproj_2,i1_3_2__anproj_2)]]).

fof(i1_3_2_tmp__anproj_2,plain,
    ( m1_subset_1(c1_3_2__anproj_2,k1_numbers)
   => ! [A] : 
        ( m1_subset_1(A,k1_numbers)
       => ! [B] : 
            ( m1_subset_1(B,k1_numbers)
           => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c1_3_2__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,A)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,B)) = k1_rlvect_1(c1_3__anproj_2)
             => ( c1_3_2__anproj_2 = 0
                & A = 0
                & B = 0 ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2]),discharge_asm(discharge,[dt_c1_3_2__anproj_2])],[dt_c1_3_2__anproj_2,i1_3_2__anproj_2]),
    [interesting(0.8),e3_3__anproj_2]).

fof(e3_3__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,A),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,B)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,C)) = k1_rlvect_1(c1_3__anproj_2)
               => ( A = 0
                  & B = 0
                  & C = 0 ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[i1_3_2_tmp__anproj_2,dh_c1_3_2__anproj_2]),
    [interesting(0.8),file(anproj_2,e3_3__anproj_2),[file(anproj_2,e3_3__anproj_2)]]).

fof(dh_c1_3_1__anproj_2,definition,
    ( ( m1_subset_1(c1_3_1__anproj_2,k1_numbers)
     => ! [A] : 
          ( m1_subset_1(A,k1_numbers)
         => ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,A)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,B)) = k1_rlvect_1(c1_3__anproj_2)
               => ( c1_3_1__anproj_2 = 0
                  & A = 0
                  & B = 0 ) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,k1_numbers)
       => ! [D] : 
            ( m1_subset_1(D,k1_numbers)
           => ! [E] : 
                ( m1_subset_1(E,k1_numbers)
               => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,C),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,D)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,E)) = k1_rlvect_1(c1_3__anproj_2)
                 => ( C = 0
                    & D = 0
                    & E = 0 ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3_1__anproj_2),file(anproj_2,c1_3_1__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c1_3_1__anproj_2)]).

fof(dh_c2_3_1__anproj_2,definition,
    ( ( m1_subset_1(c2_3_1__anproj_2,k1_numbers)
     => ! [A] : 
          ( m1_subset_1(A,k1_numbers)
         => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,A)) = k1_rlvect_1(c1_3__anproj_2)
           => ( c1_3_1__anproj_2 = 0
              & c2_3_1__anproj_2 = 0
              & A = 0 ) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k1_numbers)
       => ! [C] : 
            ( m1_subset_1(C,k1_numbers)
           => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,B)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,C)) = k1_rlvect_1(c1_3__anproj_2)
             => ( c1_3_1__anproj_2 = 0
                & B = 0
                & C = 0 ) ) ) ) ),
    introduced(definition,[new_symbol(c2_3_1__anproj_2),file(anproj_2,c2_3_1__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c2_3_1__anproj_2)]).

fof(dh_c3_3_1__anproj_2,definition,
    ( ( m1_subset_1(c3_3_1__anproj_2,k1_numbers)
     => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2)) = k1_rlvect_1(c1_3__anproj_2)
       => ( c1_3_1__anproj_2 = 0
          & c2_3_1__anproj_2 = 0
          & c3_3_1__anproj_2 = 0 ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_numbers)
       => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,A)) = k1_rlvect_1(c1_3__anproj_2)
         => ( c1_3_1__anproj_2 = 0
            & c2_3_1__anproj_2 = 0
            & A = 0 ) ) ) ),
    introduced(definition,[new_symbol(c3_3_1__anproj_2),file(anproj_2,c3_3_1__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c3_3_1__anproj_2)]).

fof(e1_3_1__anproj_2,assumption,(
    k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2)) = k1_rlvect_1(c1_3__anproj_2) ),
    introduced(assumption,[file(anproj_2,e1_3_1__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,e1_3_1__anproj_2)]).

fof(dt_c1_3_1__anproj_2,assumption,(
    m1_subset_1(c1_3_1__anproj_2,k1_numbers) ),
    introduced(assumption,[file(anproj_2,c1_3_1__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c1_3_1__anproj_2)]).

fof(dt_c2_3_1__anproj_2,assumption,(
    m1_subset_1(c2_3_1__anproj_2,k1_numbers) ),
    introduced(assumption,[file(anproj_2,c2_3_1__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c2_3_1__anproj_2)]).

fof(dt_c3_3_1__anproj_2,assumption,(
    m1_subset_1(c3_3_1__anproj_2,k1_numbers) ),
    introduced(assumption,[file(anproj_2,c3_3_1__anproj_2)]),
    [interesting(0.65),axiom,file(anproj_2,c3_3_1__anproj_2)]).

fof(d6_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ),
    file(rlvect_1,d6_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,d6_rlvect_1)]).

fof(e1_3_1_1__anproj_2,plain,(
    k1_rlvect_1(c1_3__anproj_2) = k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3_1__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,fc6_membered,rc1_membered,t1_subset,cc10_membered,cc11_membered,cc15_membered,cc4_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,dt_k1_numbers,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k2_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3_1__anproj_2,d6_rlvect_1]),
    [interesting(0.5),file(anproj_2,e1_3_1_1__anproj_2),[file(anproj_2,e1_3_1_1__anproj_2)]]).

fof(e2_3_1_1__anproj_2,plain,(
    k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)) = k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2),k1_rlvect_1(c1_3__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,fc6_membered,rc1_membered,t1_subset,cc10_membered,cc11_membered,cc15_membered,cc4_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,dt_k1_numbers,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k2_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,t10_rlvect_1]),
    [interesting(0.5),file(anproj_2,e2_3_1_1__anproj_2),[file(anproj_2,e2_3_1_1__anproj_2)]]).

fof(e3_3_1_1__anproj_2,plain,(
    k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2),k1_rlvect_1(c1_3__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)) = k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,0)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,fc2_membered,spc0_numerals,spc0_boole,t23_rlvect_1]),
    [interesting(0.5),file(anproj_2,e3_3_1_1__anproj_2),[file(anproj_2,e3_3_1_1__anproj_2)]]).

fof(e2_3_1__anproj_2,plain,(
    k1_rlvect_1(c1_3__anproj_2) = k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,0)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)) ),
    inference(iterative_eq,[status(thm),assumptions([e1_3_1__anproj_2,dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2])],[e1_3_1_1__anproj_2,e2_3_1_1__anproj_2,e3_3_1_1__anproj_2]),
    [interesting(0.65),file(anproj_2,e2_3_1__anproj_2),[file(anproj_2,e2_3_1__anproj_2)]]).

fof(e3_3_1__anproj_2,plain,
    ( c1_3_1__anproj_2 = 0
    & c2_3_1__anproj_2 = 0
    & c3_3_1__anproj_2 = 0 ),
    inference(mizar_by,[status(thm),assumptions([e1_3_1__anproj_2,dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l2_rlvect_1,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,fc2_membered,spc0_numerals,spc0_boole,e2_3_1__anproj_2,e1_3__anproj_2]),
    [interesting(0.65),file(anproj_2,e3_3_1__anproj_2),[file(anproj_2,e3_3_1__anproj_2)]]).

fof(i5_3_1__anproj_2,theorem,(
    $true ),
    introduced(tautology,[file(anproj_2,i5_3_1__anproj_2)]),
    [interesting(0.65),trivial,file(anproj_2,i5_3_1__anproj_2)]).

fof(i4_3_1__anproj_2,plain,
    ( c1_3_1__anproj_2 = 0
    & c2_3_1__anproj_2 = 0
    & c3_3_1__anproj_2 = 0 ),
    inference(conclusion,[status(thm),assumptions([e1_3_1__anproj_2,dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[e3_3_1__anproj_2,i5_3_1__anproj_2]),
    [interesting(0.65),file(anproj_2,i4_3_1__anproj_2),[file(anproj_2,i4_3_1__anproj_2)]]).

fof(i3_3_1__anproj_2,plain,
    ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2)) = k1_rlvect_1(c1_3__anproj_2)
   => ( c1_3_1__anproj_2 = 0
      & c2_3_1__anproj_2 = 0
      & c3_3_1__anproj_2 = 0 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3__anproj_2,dt_c3_3_1__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2]),discharge_asm(discharge,[e1_3_1__anproj_2])],[e1_3_1__anproj_2,i4_3_1__anproj_2]),
    [interesting(0.65),file(anproj_2,i3_3_1__anproj_2),[file(anproj_2,i3_3_1__anproj_2)]]).

fof(i3_3_1_tmp__anproj_2,plain,
    ( m1_subset_1(c3_3_1__anproj_2,k1_numbers)
   => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,c3_3_1__anproj_2)) = k1_rlvect_1(c1_3__anproj_2)
     => ( c1_3_1__anproj_2 = 0
        & c2_3_1__anproj_2 = 0
        & c3_3_1__anproj_2 = 0 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2]),discharge_asm(discharge,[dt_c3_3_1__anproj_2])],[dt_c3_3_1__anproj_2,i3_3_1__anproj_2]),
    [interesting(0.65),i2_3_1__anproj_2]).

fof(i2_3_1__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,A)) = k1_rlvect_1(c1_3__anproj_2)
       => ( c1_3_1__anproj_2 = 0
          & c2_3_1__anproj_2 = 0
          & A = 0 ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c2_3_1__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[i3_3_1_tmp__anproj_2,dh_c3_3_1__anproj_2]),
    [interesting(0.65),file(anproj_2,i2_3_1__anproj_2),[file(anproj_2,i2_3_1__anproj_2)]]).

fof(i2_3_1_tmp__anproj_2,plain,
    ( m1_subset_1(c2_3_1__anproj_2,k1_numbers)
   => ! [A] : 
        ( m1_subset_1(A,k1_numbers)
       => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,c2_3_1__anproj_2)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,A)) = k1_rlvect_1(c1_3__anproj_2)
         => ( c1_3_1__anproj_2 = 0
            & c2_3_1__anproj_2 = 0
            & A = 0 ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2]),discharge_asm(discharge,[dt_c2_3_1__anproj_2])],[dt_c2_3_1__anproj_2,i2_3_1__anproj_2]),
    [interesting(0.65),i1_3_1__anproj_2]).

fof(i1_3_1__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,A)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,B)) = k1_rlvect_1(c1_3__anproj_2)
           => ( c1_3_1__anproj_2 = 0
              & A = 0
              & B = 0 ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c1_3_1__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[i2_3_1_tmp__anproj_2,dh_c2_3_1__anproj_2]),
    [interesting(0.65),file(anproj_2,i1_3_1__anproj_2),[file(anproj_2,i1_3_1__anproj_2)]]).

fof(i1_3_1_tmp__anproj_2,plain,
    ( m1_subset_1(c1_3_1__anproj_2,k1_numbers)
   => ! [A] : 
        ( m1_subset_1(A,k1_numbers)
       => ! [B] : 
            ( m1_subset_1(B,k1_numbers)
           => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,c1_3_1__anproj_2),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,A)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,B)) = k1_rlvect_1(c1_3__anproj_2)
             => ( c1_3_1__anproj_2 = 0
                & A = 0
                & B = 0 ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2]),discharge_asm(discharge,[dt_c1_3_1__anproj_2])],[dt_c1_3_1__anproj_2,i1_3_1__anproj_2]),
    [interesting(0.8),e2_3__anproj_2]).

fof(e2_3__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,A),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,B)),k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,C)) = k1_rlvect_1(c1_3__anproj_2)
               => ( A = 0
                  & B = 0
                  & C = 0 ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[i1_3_1_tmp__anproj_2,dh_c1_3_1__anproj_2]),
    [interesting(0.8),file(anproj_2,e2_3__anproj_2),[file(anproj_2,e2_3__anproj_2)]]).

fof(t1_anproj_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ! [E] : 
                        ( m1_subset_1(E,k1_numbers)
                       => ! [F] : 
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] : 
                                ( m1_subset_1(G,k1_numbers)
                               => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
                                 => ( E = 0
                                    & F = 0
                                    & G = 0 ) ) ) ) )
                   => ( v8_rlvect_1(B,A)
                      & v8_rlvect_1(C,A)
                      & v8_rlvect_1(D,A)
                      & ~ r2_anproj_1(A,B,C,D)
                      & ~ r1_anproj_1(A,B,C) ) ) ) ) ) ) ),
    file(anproj_2,t1_anproj_2),
    [interesting(0.9),axiom,file(anproj_2,t1_anproj_2)]).

fof(e4_3__anproj_2,plain,
    ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
    & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
    & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
    & v8_rlvect_1(c4_3__anproj_2,c1_3__anproj_2)
    & v8_rlvect_1(c5_3__anproj_2,c1_3__anproj_2)
    & ~ r1_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2)
    & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,c4_3__anproj_2)
    & ~ r2_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2,c2_3__anproj_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,fc2_membered,spc0_numerals,spc0_boole,e3_3__anproj_2,e2_3__anproj_2,t1_anproj_2]),
    [interesting(0.8),file(anproj_2,e4_3__anproj_2),[file(anproj_2,e4_3__anproj_2)]]).

fof(i7_3__anproj_2,theorem,(
    $true ),
    introduced(tautology,[file(anproj_2,i7_3__anproj_2)]),
    [interesting(0.8),trivial,file(anproj_2,i7_3__anproj_2)]).

fof(i6_3__anproj_2,plain,
    ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
    & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
    & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
    & v8_rlvect_1(c4_3__anproj_2,c1_3__anproj_2)
    & v8_rlvect_1(c5_3__anproj_2,c1_3__anproj_2)
    & ~ r1_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2)
    & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,c4_3__anproj_2)
    & ~ r2_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2,c2_3__anproj_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2,e1_3__anproj_2])],[e4_3__anproj_2,i7_3__anproj_2]),
    [interesting(0.8),file(anproj_2,i6_3__anproj_2),[file(anproj_2,i6_3__anproj_2)]]).

fof(i5_3__anproj_2,plain,
    ( ! [A] : 
        ( m1_subset_1(A,k1_numbers)
       => ! [B] : 
            ( m1_subset_1(B,k1_numbers)
           => ! [C] : 
                ( m1_subset_1(C,k1_numbers)
               => ! [D] : 
                    ( m1_subset_1(D,k1_numbers)
                   => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,A),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,B)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,C)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,D)) = k1_rlvect_1(c1_3__anproj_2)
                     => ( A = 0
                        & B = 0
                        & C = 0
                        & D = 0 ) ) ) ) ) )
   => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
      & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
      & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
      & v8_rlvect_1(c4_3__anproj_2,c1_3__anproj_2)
      & v8_rlvect_1(c5_3__anproj_2,c1_3__anproj_2)
      & ~ r1_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2)
      & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,c4_3__anproj_2)
      & ~ r2_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2,c2_3__anproj_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2,dt_c5_3__anproj_2]),discharge_asm(discharge,[e1_3__anproj_2])],[e1_3__anproj_2,i6_3__anproj_2]),
    [interesting(0.8),file(anproj_2,i5_3__anproj_2),[file(anproj_2,i5_3__anproj_2)]]).

fof(i5_3_tmp__anproj_2,plain,
    ( m1_subset_1(c5_3__anproj_2,u1_struct_0(c1_3__anproj_2))
   => ( ! [A] : 
          ( m1_subset_1(A,k1_numbers)
         => ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,k1_numbers)
                     => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,A),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,B)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,C)),k3_rlvect_1(c1_3__anproj_2,c5_3__anproj_2,D)) = k1_rlvect_1(c1_3__anproj_2)
                       => ( A = 0
                          & B = 0
                          & C = 0
                          & D = 0 ) ) ) ) ) )
     => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
        & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
        & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
        & v8_rlvect_1(c4_3__anproj_2,c1_3__anproj_2)
        & v8_rlvect_1(c5_3__anproj_2,c1_3__anproj_2)
        & ~ r1_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2)
        & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,c4_3__anproj_2)
        & ~ r2_anproj_1(c1_3__anproj_2,c4_3__anproj_2,c5_3__anproj_2,c2_3__anproj_2) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2]),discharge_asm(discharge,[dt_c5_3__anproj_2])],[dt_c5_3__anproj_2,i5_3__anproj_2]),
    [interesting(0.8),i4_3__anproj_2]).

fof(i4_3__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
     => ( ! [B] : 
            ( m1_subset_1(B,k1_numbers)
           => ! [C] : 
                ( m1_subset_1(C,k1_numbers)
               => ! [D] : 
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] : 
                        ( m1_subset_1(E,k1_numbers)
                       => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,B),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,C)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,D)),k3_rlvect_1(c1_3__anproj_2,A,E)) = k1_rlvect_1(c1_3__anproj_2)
                         => ( B = 0
                            & C = 0
                            & D = 0
                            & E = 0 ) ) ) ) ) )
       => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
          & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
          & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
          & v8_rlvect_1(c4_3__anproj_2,c1_3__anproj_2)
          & v8_rlvect_1(A,c1_3__anproj_2)
          & ~ r1_anproj_1(c1_3__anproj_2,c4_3__anproj_2,A)
          & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,c4_3__anproj_2)
          & ~ r2_anproj_1(c1_3__anproj_2,c4_3__anproj_2,A,c2_3__anproj_2) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2,dt_c4_3__anproj_2])],[i5_3_tmp__anproj_2,dh_c5_3__anproj_2]),
    [interesting(0.8),file(anproj_2,i4_3__anproj_2),[file(anproj_2,i4_3__anproj_2)]]).

fof(i4_3_tmp__anproj_2,plain,
    ( m1_subset_1(c4_3__anproj_2,u1_struct_0(c1_3__anproj_2))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
       => ( ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] : 
                          ( m1_subset_1(E,k1_numbers)
                         => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,B),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,C)),k3_rlvect_1(c1_3__anproj_2,c4_3__anproj_2,D)),k3_rlvect_1(c1_3__anproj_2,A,E)) = k1_rlvect_1(c1_3__anproj_2)
                           => ( B = 0
                              & C = 0
                              & D = 0
                              & E = 0 ) ) ) ) ) )
         => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
            & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
            & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
            & v8_rlvect_1(c4_3__anproj_2,c1_3__anproj_2)
            & v8_rlvect_1(A,c1_3__anproj_2)
            & ~ r1_anproj_1(c1_3__anproj_2,c4_3__anproj_2,A)
            & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,c4_3__anproj_2)
            & ~ r2_anproj_1(c1_3__anproj_2,c4_3__anproj_2,A,c2_3__anproj_2) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2]),discharge_asm(discharge,[dt_c4_3__anproj_2])],[dt_c4_3__anproj_2,i4_3__anproj_2]),
    [interesting(0.8),i3_3__anproj_2]).

fof(i3_3__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_3__anproj_2))
         => ( ! [C] : 
                ( m1_subset_1(C,k1_numbers)
               => ! [D] : 
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] : 
                        ( m1_subset_1(E,k1_numbers)
                       => ! [F] : 
                            ( m1_subset_1(F,k1_numbers)
                           => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,C),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,D)),k3_rlvect_1(c1_3__anproj_2,A,E)),k3_rlvect_1(c1_3__anproj_2,B,F)) = k1_rlvect_1(c1_3__anproj_2)
                             => ( C = 0
                                & D = 0
                                & E = 0
                                & F = 0 ) ) ) ) ) )
           => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
              & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
              & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
              & v8_rlvect_1(A,c1_3__anproj_2)
              & v8_rlvect_1(B,c1_3__anproj_2)
              & ~ r1_anproj_1(c1_3__anproj_2,A,B)
              & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,A)
              & ~ r2_anproj_1(c1_3__anproj_2,A,B,c2_3__anproj_2) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2,dt_c3_3__anproj_2])],[i4_3_tmp__anproj_2,dh_c4_3__anproj_2]),
    [interesting(0.8),file(anproj_2,i3_3__anproj_2),[file(anproj_2,i3_3__anproj_2)]]).

fof(i3_3_tmp__anproj_2,plain,
    ( m1_subset_1(c3_3__anproj_2,u1_struct_0(c1_3__anproj_2))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_3__anproj_2))
           => ( ! [C] : 
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] : 
                          ( m1_subset_1(E,k1_numbers)
                         => ! [F] : 
                              ( m1_subset_1(F,k1_numbers)
                             => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,C),k3_rlvect_1(c1_3__anproj_2,c3_3__anproj_2,D)),k3_rlvect_1(c1_3__anproj_2,A,E)),k3_rlvect_1(c1_3__anproj_2,B,F)) = k1_rlvect_1(c1_3__anproj_2)
                               => ( C = 0
                                  & D = 0
                                  & E = 0
                                  & F = 0 ) ) ) ) ) )
             => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
                & v8_rlvect_1(c3_3__anproj_2,c1_3__anproj_2)
                & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2)
                & v8_rlvect_1(A,c1_3__anproj_2)
                & v8_rlvect_1(B,c1_3__anproj_2)
                & ~ r1_anproj_1(c1_3__anproj_2,A,B)
                & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,c3_3__anproj_2,A)
                & ~ r2_anproj_1(c1_3__anproj_2,A,B,c2_3__anproj_2) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2]),discharge_asm(discharge,[dt_c3_3__anproj_2])],[dt_c3_3__anproj_2,i3_3__anproj_2]),
    [interesting(0.8),i2_3__anproj_2]).

fof(i2_3__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_3__anproj_2))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_3__anproj_2))
             => ( ! [D] : 
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] : 
                        ( m1_subset_1(E,k1_numbers)
                       => ! [F] : 
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] : 
                                ( m1_subset_1(G,k1_numbers)
                               => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,D),k3_rlvect_1(c1_3__anproj_2,A,E)),k3_rlvect_1(c1_3__anproj_2,B,F)),k3_rlvect_1(c1_3__anproj_2,C,G)) = k1_rlvect_1(c1_3__anproj_2)
                                 => ( D = 0
                                    & E = 0
                                    & F = 0
                                    & G = 0 ) ) ) ) ) )
               => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
                  & v8_rlvect_1(A,c1_3__anproj_2)
                  & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,A)
                  & v8_rlvect_1(B,c1_3__anproj_2)
                  & v8_rlvect_1(C,c1_3__anproj_2)
                  & ~ r1_anproj_1(c1_3__anproj_2,B,C)
                  & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,A,B)
                  & ~ r2_anproj_1(c1_3__anproj_2,B,C,c2_3__anproj_2) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2,dt_c2_3__anproj_2])],[i3_3_tmp__anproj_2,dh_c3_3__anproj_2]),
    [interesting(0.8),file(anproj_2,i2_3__anproj_2),[file(anproj_2,i2_3__anproj_2)]]).

fof(i2_3_tmp__anproj_2,plain,
    ( m1_subset_1(c2_3__anproj_2,u1_struct_0(c1_3__anproj_2))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_3__anproj_2))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_3__anproj_2))
               => ( ! [D] : 
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] : 
                          ( m1_subset_1(E,k1_numbers)
                         => ! [F] : 
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,c2_3__anproj_2,D),k3_rlvect_1(c1_3__anproj_2,A,E)),k3_rlvect_1(c1_3__anproj_2,B,F)),k3_rlvect_1(c1_3__anproj_2,C,G)) = k1_rlvect_1(c1_3__anproj_2)
                                   => ( D = 0
                                      & E = 0
                                      & F = 0
                                      & G = 0 ) ) ) ) ) )
                 => ( v8_rlvect_1(c2_3__anproj_2,c1_3__anproj_2)
                    & v8_rlvect_1(A,c1_3__anproj_2)
                    & ~ r1_anproj_1(c1_3__anproj_2,c2_3__anproj_2,A)
                    & v8_rlvect_1(B,c1_3__anproj_2)
                    & v8_rlvect_1(C,c1_3__anproj_2)
                    & ~ r1_anproj_1(c1_3__anproj_2,B,C)
                    & ~ r2_anproj_1(c1_3__anproj_2,c2_3__anproj_2,A,B)
                    & ~ r2_anproj_1(c1_3__anproj_2,B,C,c2_3__anproj_2) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__anproj_2]),discharge_asm(discharge,[dt_c2_3__anproj_2])],[dt_c2_3__anproj_2,i2_3__anproj_2]),
    [interesting(0.8),i1_3__anproj_2]).

fof(i1_3__anproj_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_3__anproj_2))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_3__anproj_2))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(c1_3__anproj_2))
                 => ( ! [E] : 
                        ( m1_subset_1(E,k1_numbers)
                       => ! [F] : 
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] : 
                                ( m1_subset_1(G,k1_numbers)
                               => ! [H] : 
                                    ( m1_subset_1(H,k1_numbers)
                                   => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,A,E),k3_rlvect_1(c1_3__anproj_2,B,F)),k3_rlvect_1(c1_3__anproj_2,C,G)),k3_rlvect_1(c1_3__anproj_2,D,H)) = k1_rlvect_1(c1_3__anproj_2)
                                     => ( E = 0
                                        & F = 0
                                        & G = 0
                                        & H = 0 ) ) ) ) ) )
                   => ( v8_rlvect_1(A,c1_3__anproj_2)
                      & v8_rlvect_1(B,c1_3__anproj_2)
                      & ~ r1_anproj_1(c1_3__anproj_2,A,B)
                      & v8_rlvect_1(C,c1_3__anproj_2)
                      & v8_rlvect_1(D,c1_3__anproj_2)
                      & ~ r1_anproj_1(c1_3__anproj_2,C,D)
                      & ~ r2_anproj_1(c1_3__anproj_2,A,B,C)
                      & ~ r2_anproj_1(c1_3__anproj_2,C,D,A) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__anproj_2])],[i2_3_tmp__anproj_2,dh_c2_3__anproj_2]),
    [interesting(0.8),file(anproj_2,i1_3__anproj_2),[file(anproj_2,i1_3__anproj_2)]]).

fof(i1_3_tmp__anproj_2,plain,
    ( ( ~ v3_struct_0(c1_3__anproj_2)
      & v3_rlvect_1(c1_3__anproj_2)
      & v4_rlvect_1(c1_3__anproj_2)
      & v5_rlvect_1(c1_3__anproj_2)
      & v6_rlvect_1(c1_3__anproj_2)
      & v7_rlvect_1(c1_3__anproj_2)
      & l2_rlvect_1(c1_3__anproj_2) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__anproj_2))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_3__anproj_2))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_3__anproj_2))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(c1_3__anproj_2))
                   => ( ! [E] : 
                          ( m1_subset_1(E,k1_numbers)
                         => ! [F] : 
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_numbers)
                                 => ! [H] : 
                                      ( m1_subset_1(H,k1_numbers)
                                     => ( k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k4_rlvect_1(c1_3__anproj_2,k3_rlvect_1(c1_3__anproj_2,A,E),k3_rlvect_1(c1_3__anproj_2,B,F)),k3_rlvect_1(c1_3__anproj_2,C,G)),k3_rlvect_1(c1_3__anproj_2,D,H)) = k1_rlvect_1(c1_3__anproj_2)
                                       => ( E = 0
                                          & F = 0
                                          & G = 0
                                          & H = 0 ) ) ) ) ) )
                     => ( v8_rlvect_1(A,c1_3__anproj_2)
                        & v8_rlvect_1(B,c1_3__anproj_2)
                        & ~ r1_anproj_1(c1_3__anproj_2,A,B)
                        & v8_rlvect_1(C,c1_3__anproj_2)
                        & v8_rlvect_1(D,c1_3__anproj_2)
                        & ~ r1_anproj_1(c1_3__anproj_2,C,D)
                        & ~ r2_anproj_1(c1_3__anproj_2,A,B,C)
                        & ~ r2_anproj_1(c1_3__anproj_2,C,D,A) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__anproj_2])],[dt_c1_3__anproj_2,i1_3__anproj_2]),
    [interesting(1),t2_anproj_2]).

fof(t2_anproj_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ! [F] : 
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] : 
                                ( m1_subset_1(G,k1_numbers)
                               => ! [H] : 
                                    ( m1_subset_1(H,k1_numbers)
                                   => ! [I] : 
                                        ( m1_subset_1(I,k1_numbers)
                                       => ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
                                         => ( F = 0
                                            & G = 0
                                            & H = 0
                                            & I = 0 ) ) ) ) ) )
                       => ( v8_rlvect_1(B,A)
                          & v8_rlvect_1(C,A)
                          & ~ r1_anproj_1(A,B,C)
                          & v8_rlvect_1(D,A)
                          & v8_rlvect_1(E,A)
                          & ~ r1_anproj_1(A,D,E)
                          & ~ r2_anproj_1(A,B,C,D)
                          & ~ r2_anproj_1(A,D,E,B) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__anproj_2,dh_c1_3__anproj_2]),
    [interesting(1),file(anproj_2,t2_anproj_2),[file(anproj_2,t2_anproj_2)]]).